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Physics 1212 Exam #4D (Final) Instructions:

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Physics 1212 Exam #4D (Final) Instructions:
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
Physics 1212
Exam #4D (Final)
Instructions:
This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of your
formula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet,
except for your name: it must be handed in, signed but clean, with your exam.
There is space after each question to show your work; if you need more space, you may use
the back of the page, or request more paper. Please clearly indicate where your work for
each problem is. Underline or draw a box around your final answer.
The exam consists of four sections. Read all the questions at the start so that you can
allocate your time wisely. Do easy ones first!
You may not share your calculator. The use of cell phones or any other electronic devices (besides calculators) is prohibited. All such gadgets must be turned off and put away
throughout the exam.
• Do not open the exam until told to begin.
• You have the one entire class period to finish the exam.
• Put your last name on every page of the exam and on the formula sheet.
• You must provide explanations and/or show work legibly to receive full credit for
Sections II and III.
• Make sure that your answers include appropriate units and significant digits. (Note:
For intermediate steps in your calculation, it’s best to carry more significant digits.)
• Fundamental constants and unit prefixes are on the Formula Sheet, last page.
By signing below, you indicate that you understand the instructions for this exam and agree
to abide by them. You also certify that you will personally uphold the university’s standards
of academic honesty for this exam, and will not tolerate any violations of these standards by
others. Unsigned exams will not be graded.
Signature:
UGACard #:
c 2015 University of Georgia. Unauthorized duplication or distribution prohibited.
Copyright Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Section
I
Score
/60
II
/35
Name:
III
/35
IV
/35
V
/35
VI
/10
I: Multiple-Choice Questions (60 points)
For each question below, choose the single best response and write the corresponding
capital letter in the box provided. There is no penalty for guessing the wrong answer.
1. A diffraction grating is illuminated with a laser beam at normal incidence. A 3rd order
principal intensity maximum is observed at an angle θ3 = 39.050o , measured from
the central axis, and sin θ3 = 0.63. How many principal maxima, total, including the
central maximum, can be observed across the entire, very wide (infinite-width) screen,
i.e., between θ = −90o and θ = +90o ?
A.
B.
C.
D.
E.
11
9
6
7
5
2. In an electric generator, a single metallic wire loop, enclosing an area of 5cm2 and
~ at 700RPM, produces a maximum induced
spinning in a uniform magnetic field B
electromotoric force (EMF) of 6mV. What is the maximum induced EMF in a loop of
~
10cm2 area, spinning at 2100RPM in the same B-field?
A.
B.
C.
D.
E.
48mV
1mV
36mV
9mV
4.5mV
c 2015 University of Georgia.
Copyright 2
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
3. Visible light has a range of wavelengths from 400nm (violet) to 700nm (red) in vacuum.
A beam of electromagnetic waves with a frequency of 714.3THz in air travels from air
into water, with indices of refraction nAir = 1.00 and nWater = 1.333. To an under-water
observer, the beam while traveling in water will
A. have a wavelength of 420.0nm, have a frequency of 535.9THz, and be visible to
the human eye;
B. have a wavelength of 315.1nm, have the same frequency as in air, and be visible
to the human eye.
C. have a wavelength of 559.9nm, have the same frequency as in air, and be visible
to the human eye;
D. have a wavelength of 315.1nm, have the same frequency as in air, and be invisible
to the human eye;
E. have a wavelength of 315.1nm, have a frequency of 952.2THz, and be invisible
to the human eye;
4. In the figure below, Q1 and Q2 are positive point charges with Q1 and Q2 being of
comparable magnitude, and Q1 > Q2 . The point P and the locations of Q1 and Q2
form the three corners of a square. Which arrow drawn at P could correctly represent
~ generated by Q1 and Q2 at P ?
the electric field vector E
(C)
P
(D)
Q2
(E)
(A)
Fig. 2.30
(B)
Q1
A.
B.
C.
D.
c 2015 University of Georgia.
Copyright E.
3
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
5. Two large, metallic, planar, parallel, charged capacitor plates have an electric potential
difference of ∆V = V2 − V1 = −2500V, where V1 and V2 are the electric potentials on
the left and right plate, respectively, as shown here:
Plate 1:
Plate 2:
Fig. 2.32
An electron is shot through a small hole in the left plate, into the space between the
two plates. The electron, while traveling from the left to the right plate, ...
A. will lose 4.0 × 10−16 J in kinetic energy between left and right plate, provided it
reaches the right plate.
B. will gain 4.0 × 10−16 J in kinetic energy between left and right plate.
C. must have a kinetic energy of at least 8.0 × 10−16 J, as it passes through the left
plate, in order to reach the right plate.
D. will gain 8.0 × 10−16 J in kinetic energy between left and right plate.
E. will gain 2.0 × 10−16 J in kinetic energy between left and right plate.
~ Which of
6. A small particle of electric charge q is traveling in a uniform magnetic field, B.
~
the following figure panels could correctly represent the B-field direction; the magnetic
force, F~ , exerted on the particle by the magnetic field; and either the particle’s velocity
vector, ~v , or its q~v -vector,
whichever is indicated in the panel.
Fig. 3.54
v
F
B
(1)
A.
B.
C.
D.
E.
F
F
B
B
B
qv
(2)
qv
(3)
F
v
B
F
(4)
v
(5)
Panel (1), but only if q is positive.
Both Panels (2) and (3), but only if q is negative.
Panel (4), but only if q is positive.
Panel (3), regardless of the sign of q.
Panel (5), but only if q is positive.
c 2015 University of Georgia.
Copyright 4
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
7. Two very long thin straight wires running parallel to the z-axis carry currents I1 (in
−z-direction) and I2 (in +z-direction). The intersections of the wires with the x − yplane and point P form 3 corners of a square, as shown here:
Fig. 3.39
(C)
y
(D)
(E)
(B)
P
(A)
I2
I1
x
y
x-y-Plane View
x
z
Assuming |I1 | < |I2 |/2, which arrow drawn at point P in the x − y-plane could cor~ produced by I1 and I2 at P ?
rectly represent the magnetic field vector B
A.
B.
C.
D.
E.
8. In the circuit fragment shown below, given currents are I1 = +7A and I3 = +3A; and
resistances are Rb = 6 Ω and Rc = 10 Ω. What is the electrical potential difference
Vbc ≡ Vb − Vc between points b and c in the circuit?
I1
I3
a
Fig. 3.60
Rc
c
I2
Rb
A.
B.
C.
D.
E.
+6V
−54V
−30V
+54V
−6V
b
Arrows indicate positive current directions:
I>0 if |I| flowing into arrow direction
I<0 if |I| flowing against arrow direction
c 2015 University of Georgia.
Copyright 5
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
II: Lateral and Angular Magnification by a Single Lens (35 points)
If a small object, 1.2mm in size, is placed 2.5cm from a lens the lens produces an erect,
virtual image with a 6-fold lateral magnification.
(a) Find the image distance, d0 , and, from that, the lens’s focal length, f . Is this a
convergent or a divergent lens?
(b) Find the angular magnification achieved with this placement of the object, compared
to viewing the same object from a near-point distance of 25cm without any optical
instrument. Does the angular magnification depend on the size of the object?
(c) How far from this lens must the object be placed to produce an image with a lateral
magnification of −8. Is this a virtual or a real image? Is the image erect of inverted?
c 2015 University of Georgia.
Copyright 6
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
Work and Drawing Space for Problem II:
c 2015 University of Georgia.
Copyright 7
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
III: Electric Field from Point Charges (35 points)
A point charge of unknown amount, Q1 , is positioned at an unknown location in the x-y~ 1 ≡ [E1,x , E1,y , E1,z ] with components E1,x =
plane. It produces an electric field vector E
−3N/C, E1,y = +5N/C, E1,z = 0, at an observation point, P ≡ (xP , 0, 0) with xP = −6m, on
the x-axis.
A second point charge, Q2 = −25nC, is now added, placed at the origin, O, and both point
~ = [Ex , Ey , Ez ].
charges combined, Q1 and Q2 , then jointly produce a net electric field, E
~ at P ; its strength, |E|;
~ and its angle, θ, measured from
(a) Calculate the components of E
~ points above the x-axis, else θ < 0.
the +x-direction, with θ > 0 if E
~ 1;
On the blank page attached, make a big drawing showing: x-axis; y-axis; O; P ; E
~ 2 , produced by Q2 at P ; and E,
~ as the resultant in a vector
the field contribution E
addition parallelogram, all field vectors with their tail ends attached to P .
(b) Now Q1 is removed and an electron is placed, at rest, at point P and then released,
to accelerate subject to the electric field produced by Q2 . Find the magnitude and
direction of the electron’s acceleration, ~a, immediately after its release at P .
Then also show ~a in the drawing from (a), correctly aligned with the relevant electric
field vector.
(c) In Part (b), what is the electron’s speed, if it travels infinitely far away from Q2 ?
c 2015 University of Georgia.
Copyright 8
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
Work and Drawing Space for Problem III:
c 2015 University of Georgia.
Copyright 9
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
IV: Circuit Analysis (35 points) In the circuit shown below, assume that I1 = 6A,
I4 = 9A, R1 = 8Ω, R2 = 4Ω, R3 = 7Ω, C = 25 µF. Also assume that the capacitor is
fully charged, by the voltage drop across it, and there is no current flowing to or from either
capacitor plate.
Fig. 3.49
p
a
Io
I1
x
E
I3
q
I2
R1
IC
C
RC
y
I4
R3
R2
R4
b
(a) Find the total current, Io , flowing through the battery.
Hints: Since there’s no
current to or from the capacitor plates, what is the current IC and/or the current
through RC ? Use a junction (node) to find I2 or I3 , then another junction to find Io .
(b) Find the battery voltage E.
Hint: Use a junction to find I3 , then a loop to find E.
(c) Find the total amount of electric field energy stored in the capacitor C.
a loop to find Vy − Vx .
c 2015 University of Georgia.
Copyright Hint: Use
10
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
Work Space for Problem IV:
c 2015 University of Georgia.
Copyright 11
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
V: Flux and Induced Current in a Loop (35 points) The infinitely long
straight wire in the x-y-plane, shown below at d = 5cm from the x-axis, carries a timedependent current, I(t), flowing in the +x-direction. I(t) increases linearly with time t at a
rate of ∆I/∆t = +0.3A/s, starting with I(0) = 0 at time t = 0. A narrow rectangular wire
loop in the x-y-plane, with sidelengths a = 6cm and b = 0.25cm, is centered at the origin
O ≡ (0, 0, 0).
y
I
Fig. 4.14
y
d
b
Loop
x
z
x
a
(a) Find the current I at time t1 = 5s, and the strength and direction of the magnetic field,
~ produced by that current at the center of the loop, O ≡ (0, 0, 0), at time t1 = 5s.
B,
(b) Calculate the magnetic flux, Φm , through the loop time t1 = 5s, with the loop’s area
~ defined to point in the +z-direction. Use the magnetic field vector, B,
~ calcuvector A
~ is approximately uniform across the loop
lated at the center of the loop and assume B
area. Also calculate the rate of change of this flux, ∆Φm /∆t.
(c) Find the current, IL , induced in the loop by the time-dependent flux, Φm , assuming
the loop wire has a resistance of 0.7Ω. Does IL flow clockwise or counter-clockwise
around the loop, as seen in the plane of the drawing above?
c 2015 University of Georgia.
Copyright 12
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
Work Space for Problem V:
c 2015 University of Georgia.
Copyright 13
Physics 1212 Exam #4D (Final)
Tue., 5 May 2015
Name:
VI: Draw a Ray Diagram (Extra Credit: 10 points)
A real object is positioned to the right of a convergent lens, at a distance from the lens
which is less than the absolute value of the lens’s focal length. Use a ruler to draw a clean
ray diagram for the formation of the image, showing at least two of the principal rays, the
lens and both its focal points, the object and the image, all of them clearly labeled. Also
clearly label the incoming and the outgoing side of the lens. Is the image real or virtual?
c 2015 University of Georgia.
Copyright 14
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